CN109613823B - Nonlinear vibration isolation and impact resistance control system and method - Google Patents
Nonlinear vibration isolation and impact resistance control system and method Download PDFInfo
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Abstract
The invention discloses a nonlinear vibration isolation and impact resistance control system and a method, wherein the system comprises: vibration isolation system, vibration isolation system includes: the electromagnetic actuator consists of an upper electromagnet and a lower electromagnet which are controlled in a differential mode, the displacement sensor is arranged in the middle of each electromagnet, the displacement sensors are connected with the signal conditioning circuit, and the power amplifier is connected with a coil of each electromagnet; the electromagnetic actuator is used for carrying out suspension supporting on the supporting frame through electromagnetic force generated by the cooperative work. According to the system and the method provided by the invention, the attractive force of the electromagnetic actuator on the support frame is controlled through the high-static-low controller, the axial displacement of the support frame is adjusted, and further, the excellent vibration isolation and impact resistance can be ensured while the static bearing capacity is considered.
Description
Technical Field
The invention relates to the technical field of nonlinear vibration isolators, in particular to a nonlinear vibration isolation and impact resistance control system and method.
Background
The dynamic characteristics of the traditional passive vibration isolation system are determined once the structure is determined, and the traditional passive vibration isolation system is difficult to change again. For example, the structure of the metal rubber vibration isolator, the steel spring vibration isolator and the air cushion vibration isolator is determined, the dynamic characteristic is also determined, the vibration isolation effect is also determined, the adjustment along with the actual situation cannot be carried out, and the debugging performance is poor.
In addition, for the linear vibration isolator, a compromise is always found between the vibration isolation performance and the bearing performance of the system, and from the vibration isolation principle, in order to ensure better vibration isolation effect and vibration isolation of wide frequency bands including low frequency, the smaller the equivalent stiffness of the vibration isolation system is, the better the equivalent stiffness of the vibration isolation system is, but in order to ensure static bearing capacity, the smaller the stiffness of the vibration isolation system cannot be, otherwise, the larger displacement of a supported object under static force can be caused.
Therefore, the existing vibration isolator cannot guarantee excellent vibration isolation and impact resistance while considering the bearing capacity.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a nonlinear vibration isolation and impact resistance control system and method, wherein a high-static-low controller is used for controlling the attraction of an electromagnetic actuator to a support frame, the axial displacement of the support frame is adjusted, and the excellent vibration isolation and impact resistance are ensured while the bearing capacity is considered.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a non-linear vibration isolation and shock resistance control system comprising: a vibration isolation system, the vibration isolation system comprising: the electromagnetic actuator consists of an upper electromagnet and a lower electromagnet which are controlled in a differential mode, a displacement sensor is arranged in the middle of each electromagnet, the displacement sensors are connected with the signal conditioning circuit, and the power amplifier is connected with a coil of each electromagnet; the control system further comprises:
the first design module is used for designing a force-displacement nonlinear dynamic characteristic curve with high static and low dynamic characteristics according to different vibration and impact load working conditions, determining the size of a first displacement range and the segmentation number j of differential links, and determining the segmentation parameter set lambdaηA value of (η ═ 1, 2.. j-1);
the second design module is used for obtaining the load bearing quality required by a single electromagnetic actuator according to the number of the electromagnetic actuators and the sum of the support frame and the load quality;
first of allA setting module for setting the gain link function expression f in the high static low control algorithm according to the coefficient in the force-displacement nonlinear dynamics characteristic curvep(e)；
A second setting module, configured to set a differential parameter set k in a differential link in the high static-low control algorithm according to a damping ratio requirement of an engineering applicationdηA value of (η ═ 1, 2.. j) or setting a differential link function expression f in the high static low control algorithmd(e)；
The writing module is used for programming and writing the set high static and low control algorithm into a controller of the vibration isolation system to form a high static and low controller;
the electromagnetic actuator is used for carrying out suspension support on the supporting frame through electromagnetic force generated by the cooperative work;
the displacement sensor is used for acquiring an axial displacement signal of the supporting frame and inputting the axial displacement signal into the signal conditioning circuit;
the signal conditioning circuit is used for converting the axial displacement signal from an analog quantity to a digital quantity and inputting the digital quantity to the high-static-low controller;
the high static low controller is used for comparing the received axial displacement with a reference position to obtain a deviation value, and the gain link function expression f is usedp(e) And the differential parameter group kdη(η ═ 1,2,. j), or expression f of a function of said differential ring elementd(e) Calculating and generating a corresponding control signal, and inputting the control signal into the power amplifier;
and the power amplifier generates control current according to the control signal, controls the attractive force of the electromagnetic actuator on the supporting frame, and adjusts the axial displacement of the supporting frame.
Further, in the above non-linear vibration isolation and impact resistance control system, the first design module is further configured to: estimating the range of vibration response and impact response of the supported object;
the force-displacement nonlinear dynamics characteristic curve satisfies the following conditions: the estimated system stiffness in the region of the vibrational response near the equilibrium position is within a first range of displacement within a first range of stiffness; the system stiffness outside the region near the equilibrium position of the estimated impulse response is within a second range of displacement within a second range of stiffness; the system stiffness is the curvature of the force-displacement nonlinear dynamical characteristic curve;
the whole closed-loop control system has the force-displacement nonlinear dynamic characteristics of high static and low dynamic characteristics,
when a foundation or a supporting object is subjected to vibration load, the corresponding displacement of the foundation or the supporting object is within the first displacement range of the force-displacement nonlinear dynamic characteristic curve, the system stiffness of the vibration isolation system in the area near the equilibrium position is within a first stiffness range, according to the vibration isolation principle, the smaller the system stiffness is, the smaller the natural frequency of the vibration isolation system is, and according to the classical vibration theory, the wider the vibration isolation frequency band is, the better the vibration isolation effect is;
when impact acts on a foundation or a supporting object, the corresponding displacement of the impact is within the second displacement range of the force-displacement nonlinear dynamic characteristic curve, and the supporting force of the vibration isolation system within the second displacement range is increased/decreased in a nonlinear rapid mode along with the increase/decrease of the displacement.
Further, in the nonlinear vibration isolation and impact resistance control system as described above, the force-displacement nonlinear dynamic characteristic curve is a curve represented by a cubic function of the following formula,
y＝Ax3+Bx2+Cx+D
a, B, C, D is a coefficient of a cubic function determined from the curve, the cubic function satisfying: 3. Ax2+2·Bx+C≥0。
Further, in the nonlinear vibration isolation and impact resistance control system, the single electromagnetic actuator needs to bear the load mass meThe following relationship is satisfied:
wherein m is the sum of the support frame and the load mass, and n is the number of the electromagnetic actuators.
Further, a nonlinear vibration isolation and shock resistance control system as described above, said high static low control algorithm comprising:
and a gain link:
substituting the deviation value into the gain link function expression fp(e) Calculating gain link control quantity to adjust the rigidity of the dynamic support system;
and (3) differentiation:
comparing the deviation value multiplied by the set of differential parameters kdηCorresponding k in (η ═ 1, 2.. j)d1、kd2、kd3…kdjThen, differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system; or
Multiplying the deviation value by the differential link function expression fd(e) Then, differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system;
taking the sum of the gain link control quantity and the differential link control quantity as the total high-static low controller output quantity;
the gain link function expression fp(e) Comprises the following steps:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kxIs the force-displacement coefficient, kIForce-current coefficient, e deviation value, A, B, C constant;
different deviation values and differential parameter groups k in the differential linkdηThe corresponding relationship of (η ═ 1, 2.. j) is:
wherein λ isjAs segmentation parametersGroup, satisfies lambda1≤λ2≤λ3≤λ4≤...λj-1The number of segments j is more than or equal to 2 and the parameter set kdηThe setting of (η ═ 1, 2.. j) satisfies:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kIIs the force-current coefficient, meThe mass of the load required for a single electromagnetic actuator, kpThe rigidity coefficient is related to the deviation value as follows:
wherein k issIs the displacement sensor gain, e is the offset value, A, B, C is a constant;
the differential element function expression fd(e) Comprises the following steps:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kIIs the force-current coefficient, c is the system damping, meThe load mass required to be borne by a single electromagnetic actuator is provided, gamma is a damping ratio, and the range of gamma is more than 0 and less than 1.
Further, a nonlinear vibration isolation and shock resistance control system as described above, said signal conditioning circuit comprising: the device comprises an AD conversion module and an AD sampling module, wherein the AD conversion module is used for converting the axial displacement signal from analog quantity to digital quantity, and the AD sampling module is used for setting sampling frequency and obtaining a final sampling signal from the axial displacement signal of the digital quantity;
the displacement sensor is as follows: the displacement sensor is an inductive sensor, the upper probe and the lower probe are controlled to collect through differential motion, and when the displacement sensor is an eddy current sensor, the upper probe and the lower probe are controlled to collect through one probe.
A nonlinear vibration isolation and shock resistance control method is applied to a vibration isolation system, and the vibration isolation system comprises: the electromagnetic actuator consists of an upper electromagnet and a lower electromagnet which are controlled in a differential mode, a displacement sensor is arranged in the middle of each electromagnet, the displacement sensors are connected with the signal conditioning circuit, and the power amplifier is connected with a coil of each electromagnet; the electromagnetic actuator is used for carrying out suspension support on the supporting frame through electromagnetic force generated by the cooperative work;
the control method comprises the following steps:
s1, designing a force-displacement nonlinear dynamic characteristic curve with high static and low dynamic characteristics according to different vibration and impact load working conditions, determining the size of a first displacement range and the number j of segments of a differential link, and determining the group lambda of segment parametersηA value of (η ═ 1, 2.. j-1);
s2, obtaining the load mass required to be borne by a single electromagnetic actuator according to the number of the electromagnetic actuators and the sum of the support frame and the load mass;
s3, setting a gain link function expression f in a high static low control algorithm according to the coefficient in the force-displacement nonlinear dynamic characteristic curvep(e)；
S4, setting a differential parameter group k in a differential link in the high static low control algorithm according to the damping ratio requirement of engineering applicationdηA value of (η ═ 1, 2.. j) or setting a differential link function expression f in the high static low control algorithmd(e)；
S5, programming and writing the set high static and low control algorithm into a controller of the vibration isolation system to form a high static and low controller;
s6, the displacement sensor collects an axial displacement signal of the supporting frame and inputs the axial displacement signal into the signal conditioning circuit;
s7, converting the axial displacement signal from an analog quantity to a digital quantity by the signal conditioning circuit and inputting the digital quantity to the high static low controller;
s8, the high static low controller compares the received axial displacement with a reference position to obtain a deviation value, and the gain link function expression f is usedp(e) And the differential parameter group kdη(η ═ 1,2,. j), or expression f of a function of said differential ring elementd(e) Calculating and generating a corresponding control signal, and inputting the control signal into the power amplifier;
and S9, the power amplifier generates a control current according to the control voltage and controls the attractive force of the electromagnetic actuator on the support frame.
Further, in the above method for controlling nonlinear vibration isolation and shock resistance, step S1 further includes: estimating the range of vibration response and impact response of the supported object;
the force-displacement nonlinear dynamics characteristic curve satisfies the following conditions: the estimated system stiffness in the region of the vibrational response near the equilibrium position is within a first range of displacement within a first range of stiffness; the system stiffness outside the region near the equilibrium position of the estimated impulse response is within a second range of displacement within a second range of stiffness; the system stiffness is the curvature of the force-displacement nonlinear dynamical characteristic curve;
the whole closed-loop control system has the force-displacement nonlinear dynamic characteristics of high static and low dynamic characteristics,
when a foundation or a supporting object is subjected to vibration load, the corresponding displacement of the foundation or the supporting object is within the first displacement range of the force-displacement nonlinear dynamic characteristic curve, the system stiffness of the vibration isolation system in the area near the equilibrium position is within a first stiffness range, according to the vibration isolation principle, the smaller the system stiffness is, the smaller the natural frequency of the vibration isolation system is, and according to the classical vibration theory, the wider the vibration isolation frequency band is, the better the vibration isolation effect is;
when impact acts on a foundation or a supporting object, the corresponding displacement of the impact is within the second displacement range of the force-displacement nonlinear dynamic characteristic curve, and the supporting force of the vibration isolation system within the second displacement range is increased/decreased in a nonlinear rapid mode along with the increase/decrease of the displacement.
Further, in the above non-linear vibration isolation and impact resistance control method, the force-displacement non-linear dynamic characteristic curve is a curve represented by a cubic function of the following formula,
y＝Ax3+Bx2+Cx+D
a, B, C, D is a coefficient of a cubic function determined from the curve, the cubic function satisfying: 3. Ax2+2·Bx+C≥0；
Mass m of load to be borne by a single electromagnetic actuatoreThe following relationship is satisfied:
wherein m is the sum of the support frame and the load mass, and n is the number of the electromagnetic actuators.
Further, in the above non-linear vibration isolation and shock resistance control method, the high static and low control algorithm includes:
and a gain link:
substituting the deviation value into the gain link function expression fp(e) Calculating gain link control quantity to adjust the rigidity of the dynamic support system;
and (3) differentiation:
comparing the deviation value multiplied by the set of differential parameters kdηCorresponding k in (η ═ 1, 2.. j)d1、kd2、kd3…kdjThen, differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system; or
Multiplying the deviation value by the differential link function expression fd(e) Then, differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system;
taking the sum of the gain link control quantity and the differential link control quantity as the total high-static low controller output quantity;
the gain link function expression fp(e) Comprises the following steps:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kxIs the force-displacement coefficient, kIForce-current coefficient, e deviation value, A, B, C constant;
different deviation values and differential parameter groups k in the differential linkdηThe corresponding relationship of (η ═ 1, 2.. j) is:
wherein λ isjFor the set of segmentation parameters, λ is satisfied1≤λ2≤λ3≤λ4≤...λj-1The number of segments j is more than or equal to 2 and the parameter set kdηThe setting of (η ═ 1, 2.. j) satisfies:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kIIs the force-current coefficient, meThe mass of the load required for a single electromagnetic actuator, kpThe rigidity coefficient is related to the deviation value as follows:
wherein k issIs the displacement sensor gain, e is the offset value, A, B, C is a constant;
the differential element function expression fd(e) Comprises the following steps:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kIIs the force-current coefficient, c is the system damping, meThe load mass required to be borne by a single electromagnetic actuator is provided, gamma is a damping ratio, and the range of gamma is more than 0 and less than 1.
The invention has the beneficial effects that: according to the system and the method provided by the invention, the attractive force of the electromagnetic actuator on the support frame is controlled through the high-static-low controller, the axial displacement of the support frame is adjusted, and the excellent vibration isolation and impact resistance are ensured while the bearing capacity is considered.
Drawings
Fig. 1 is a first structural schematic diagram of a nonlinear vibration isolation and shock resistance control system according to an embodiment of the present invention;
fig. 2 is a second structural schematic diagram of a nonlinear vibration isolation and shock resistance control system according to an embodiment of the present invention;
fig. 3 is a schematic flow chart of a nonlinear vibration isolation and shock resistance control method according to an embodiment of the present invention;
FIG. 4 is a block diagram of a closed loop control of a differential of an electromagnetic actuator provided in an embodiment of the present invention;
FIG. 5 is a block diagram of a closed loop control of a differential of an electromagnetic actuator provided in an embodiment of the present invention;
fig. 6 is a graph of force-displacement nonlinear dynamics provided in an embodiment of the present invention.
In the figure, 61, a controller, 62, a power amplifier, 63, a displacement sensor, 64, a signal conditioning circuit, 65, an electromagnetic actuator, 66, a radial bearing, 67 and a support frame.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
The dynamic characteristics of the traditional passive vibration isolation system are determined once the structure is determined, and the traditional passive vibration isolation system is difficult to change again. In addition, for a linear vibration isolator, there is always a compromise between the vibration isolation performance and the bearing performance of the system, because in terms of vibration isolation principle, in order to ensure better vibration isolation effect and vibration isolation of wide frequency bands including low frequency, the smaller the equivalent stiffness of the vibration isolation system is, the better the equivalent stiffness of the vibration isolation system is, but in order to ensure static bearing capacity, the stiffness of the vibration isolation system cannot be too small, otherwise, a large displacement of a supported object under static force (such as the gravity of the supported object) is caused.
In order to solve the problems, the invention provides a nonlinear vibration isolation and shock resistance control system which mainly comprises an electromagnetic actuator, a displacement sensor and a high-static-low controller. The active controllability of the electromagnetic actuator is utilized, the nonlinear dynamic characteristics of high static and low dynamic of the electromagnetic actuator are realized by using a control algorithm, the excellent vibration isolation and impact resistance can be ensured while the bearing capacity is considered, and the nonlinear dynamic supporting characteristic curve of the vibration isolator can be freely designed and changed by using the control algorithm according to actual structural parameters, so that the vibration isolator is applied to different machines and working conditions. The details are as follows.
As shown in fig. 1-2, a nonlinear vibration isolation and shock resistance control system includes: vibration isolation system 6, vibration isolation system 6 includes: the electromagnetic actuator 65 consists of an upper electromagnet and a lower electromagnet which are controlled differentially, the displacement sensor 63 is arranged in the middle of each electromagnet, the displacement sensors 63 are connected with the signal conditioning circuit 64, and the power amplifier 62 is connected with coils of each electromagnet; the control system further comprises:
the first design module 1 is used for designing a force-displacement nonlinear dynamic characteristic curve with high static and low dynamic characteristics according to different vibration and impact load working conditions, determining the size of a first displacement range and the segmentation number j of differential links, and determining the segmentation parameter set lambdaηA value of (η ═ 1, 2.. j-1); in this embodiment, j is set to 2, and the segmentation parameter set includes λ1。
The second design module 2 is used for obtaining the load bearing quality required by the single electromagnetic actuator 65 according to the number of the electromagnetic actuators 65 and the sum of the support frame 67 and the load bearing quality;
a first setting module 3, configured to set a gain link function expression f in a high-static-low control algorithm according to a coefficient in a force-displacement nonlinear dynamics characteristic curvep(e)；
A second setting module 4, configured to set a differential parameter set k in a differential link in a high static-low control algorithm according to a damping ratio requirement of an engineering applicationdη(η ═ 1, 2.. j) or setting of the differential link function expression f in the high static low control algorithmd(e) (ii) a In this embodiment, the differential parameter set comprises kd1、kd2。
The writing module 5 is used for programming and writing the set high static and low control algorithm into a controller 61 of the vibration isolation system to form a high static and low controller;
the electromagnetic actuator 65 is used for carrying out suspension support on the support frame 67 through electromagnetic force generated by the cooperative work;
the displacement sensor 63 is used for acquiring an axial displacement signal of the supporting frame 67 and inputting the axial displacement signal into the signal conditioning circuit 64;
the signal conditioning circuit 64 is used for converting the axial displacement signal from an analog quantity to a digital quantity and inputting the digital quantity into the high-static-low controller;
the high static low controller 61 is used for comparing the received axial displacement with a reference position to obtain a deviation value, and obtaining a gain link function expression fp(e) And a differential parameter set kd1、kd2Or with the expression f for the differential link functiond(e) Calculating and generating a corresponding control signal, and inputting the control signal into the power amplifier;
the power amplifier 62 generates a control current according to the control signal, controls the attractive force of the electromagnetic actuator 65 to the support 67, and adjusts the axial displacement of the support 67.
The first design module 1 is also used for: estimating the range of vibration response and impact response of the supported object;
the force-displacement nonlinear dynamics characteristic curve satisfies the following conditions: the estimated system stiffness in the region of the vibrational response near the equilibrium position is within a first range of displacement within a first range of stiffness; the system stiffness outside the region near the equilibrium position of the estimated impulse response is within a second range of displacement within a second range of stiffness; the system rigidity is the curvature of a force-displacement nonlinear dynamic characteristic curve;
the whole closed-loop control system has the force-displacement nonlinear dynamic characteristics of high static and low dynamic characteristics,
when a foundation or a supporting object is subjected to vibration load, the corresponding displacement is in the first displacement range of a force-displacement nonlinear dynamic characteristic curve, the system stiffness of the vibration isolation system in the area near the balance position is in the first stiffness range, according to the vibration isolation principle, the smaller the system stiffness is, the smaller the natural frequency of the vibration isolation system is, according to the classical vibration theory, the wider the vibration isolation frequency band is, and the better the vibration isolation effect is;
when impact is applied to the foundation or the supporting object, the corresponding displacement is in a second displacement range of the force-displacement nonlinear dynamic characteristic curve, and the supporting force of the vibration isolation system in the second displacement range is increased/decreased in a nonlinear rapid mode along with the increase/decrease of the displacement.
The force-displacement nonlinear dynamics characteristic curve is a curve expressed by a cubic function of the following formula,
y＝Ax3+Bx2+Cx+D
a, B, C, D is a coefficient of a cubic function determined from the curve, the cubic function satisfying: 3. Ax2+2·Bx+C≥0。
Mass m of load to be borne by a single electromagnetic actuatoreThe following relationship is satisfied:
wherein m is the sum of the support frame and the load mass, and n is the number of the electromagnetic actuators.
The high static low control algorithm comprises the following steps:
and a gain link:
deviation valueSubstituting gain link function expression fp(e) Calculating gain link control quantity to adjust the rigidity of the dynamic support system;
and (3) differentiation:
comparing the deviation value multiplied by a corresponding k within the set of differential parametersd1、kd2Then, differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system; or
Multiplying the deviation value by the differential link function expression fd(e) Then, differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system;
taking the sum of the gain link control quantity and the differential link control quantity as the total high-static low controller output quantity;
the gain link function expression fp(e) Comprises the following steps:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kxIs the force-displacement coefficient, kIForce-current coefficient, e deviation value, A, B, C constant;
different deviation values and differential parameter groups k in the differential linkd1、kd2The corresponding relation is as follows:
wherein λ isjFor the segmentation of the parameter set, λ in the present embodiment1The number of segments j is 2 and the set of differential parameters kd1、kd2The setting of (1) satisfies:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kIIs the force-current coefficient, meThe mass of the load required for a single electromagnetic actuator, kpThe rigidity coefficient is related to the deviation value as follows:
wherein k issIs the displacement sensor gain, e is the offset value, A, B, C is a constant;
differential element function expression fd(e) Comprises the following steps:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kIIs the force-current coefficient, c is the system damping, meThe load mass required to be borne by a single electromagnetic actuator is provided, gamma is a damping ratio, and the range of gamma is more than 0 and less than 1.
The signal conditioning circuit includes: the device comprises an AD conversion module and an AD sampling module, wherein the AD conversion module is used for converting an axial displacement signal from an analog quantity to a digital quantity, and the AD sampling module is used for setting a sampling frequency and obtaining a final sampling signal from the axial displacement signal of the digital quantity;
the displacement sensor is as follows: the inductive sensor or the eddy current sensor is used for collecting through an upper probe and a lower probe which are controlled by differential motion when the displacement sensor is the inductive sensor, and collecting through one probe when the displacement sensor is the eddy current sensor.
As shown in fig. 3, a nonlinear vibration isolation and impact resistance control method is applied to a vibration isolation system, and the vibration isolation system includes: the electromagnetic actuator consists of an upper electromagnet and a lower electromagnet which are controlled in a differential mode, the displacement sensor is arranged in the middle of each electromagnet, the displacement sensors are connected with the signal conditioning circuit, and the power amplifier is connected with a coil of each electromagnet; the electromagnetic actuator is used for carrying out suspension support on the supporting frame through electromagnetic force generated by the cooperative work;
the control method comprises the following steps:
s1, designing a force-displacement nonlinear dynamic characteristic curve with high static and low dynamic characteristics according to different vibration and impact load working conditions, determining the size of a first displacement range and the number j of segments of a differential link, and determining the group lambda of segment parametersηA value of (η ═ 1, 2.. j-1); in this embodiment, j is set to 2, and the segmentation parameter set includes λ1。
S2, obtaining the load mass required to be borne by a single electromagnetic actuator according to the number of the electromagnetic actuators and the sum of the support frame and the load mass;
s3, setting a gain link function expression f in a high static low control algorithm according to the coefficient in the force-displacement nonlinear dynamic characteristic curvep(e)；
S4, setting a differential parameter group k in a differential link in a high static low control algorithm according to the damping ratio requirement of engineering applicationdη(η ═ 1, 2.. j) or setting of the differential link function expression f in the high static low control algorithmd(e) (ii) a In this embodiment, the differential parameter set comprises kd1、kd2。
S5, programming and writing the set high static and low control algorithm into a controller of the vibration isolation system to form a high static and low controller;
s6, the displacement sensor collects the axial displacement signal of the supporting frame and inputs the axial displacement signal into the signal conditioning circuit;
s7, converting the axial displacement signal from analog quantity to digital quantity by the signal conditioning circuit and inputting the digital quantity to the high-static-low controller;
s8, the high static low controller compares the received axial displacement with the reference position to obtain a deviation value, and the deviation value is expressed according to a gain link function expression fp(e) And a differential parameter set kdη(η ═ 1,2,. j), or with the differential link function expression fd(e) Calculate and generate corresponding control signals, and willThe control signal is input into the power amplifier;
and S9, generating a control current by the power amplifier according to the control voltage, and controlling the attractive force of the electromagnetic actuator on the support.
Step S1 further includes: estimating the range of vibration response and impact response of the supported object;
the force-displacement nonlinear dynamics characteristic curve satisfies the following conditions: the estimated system stiffness in the region of the vibrational response near the equilibrium position is within a first range of displacement within a first range of stiffness; the system stiffness outside the region near the equilibrium position of the estimated impulse response is within a second range of displacement within a second range of stiffness; the system rigidity is the curvature of a force-displacement nonlinear dynamic characteristic curve;
the whole closed-loop control system has the force-displacement nonlinear dynamic characteristics of high static and low dynamic characteristics,
when a foundation or a supporting object is subjected to vibration load, the corresponding displacement is in the first displacement range of a force-displacement nonlinear dynamic characteristic curve, the system stiffness of the vibration isolation system in the area near the balance position is in the first stiffness range, according to the vibration isolation principle, the smaller the system stiffness is, the smaller the natural frequency of the vibration isolation system is, according to the classical vibration theory, the wider the vibration isolation frequency band is, and the better the vibration isolation effect is;
when impact is applied to the foundation or the supporting object, the corresponding displacement is in a second displacement range of the force-displacement nonlinear dynamic characteristic curve, and the supporting force of the vibration isolation system in the second displacement range is increased/decreased in a nonlinear rapid mode along with the increase/decrease of the displacement.
The force-displacement nonlinear dynamics characteristic curve is a curve expressed by a cubic function of the following formula,
y＝Ax3+Bx2+Cx+D
a, B, C, D is a coefficient of a cubic function determined from the curve, the cubic function satisfying: 3. Ax2+2·Bx+C≥0；
Mass m of load to be borne by a single electromagnetic actuatoreThe following relationship is satisfied:
wherein m is the sum of the support frame and the load mass, and n is the number of the electromagnetic actuators.
The high static low control algorithm comprises the following steps:
and a gain link:
substituting the deviation value into a gain link function expression fp(e) Calculating gain link control quantity to adjust the rigidity of the dynamic support system;
and (3) differentiation:
comparing the deviation value multiplied by a corresponding k within the set of differential parametersd1、kd2Then, differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system; or
Multiplying the deviation value by the differential link function expression fd(e) Then, differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system;
taking the sum of the gain link control quantity and the differential link control quantity as the total high-static low controller output quantity;
the gain link function expression fp(e) Comprises the following steps:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kxIs the force-displacement coefficient, kIForce-current coefficient, e deviation value, A, B, C constant;
different deviation values and differential parameter groups k in the differential linkd1、kd2The corresponding relation is as follows:
wherein，λjFor the segmentation of the parameter set, λ in the present embodiment1The number of segments j is 2 and the parameter set kd1、kd2The setting of (1) satisfies:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kIIs the force-current coefficient, meThe mass of the load required for a single electromagnetic actuator, kpThe rigidity coefficient is related to the deviation value as follows:
wherein k issIs the displacement sensor gain, e is the offset value, A, B, C is a constant;
differential element function expression fd(e) Comprises the following steps:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kIIs the force-current coefficient, c is the system damping, meThe load mass required to be borne by a single electromagnetic actuator is provided, gamma is a damping ratio, and the range of gamma is more than 0 and less than 1.
As shown in fig. 2, the electromagnetic actuator differential closed-loop control principle: the upper electromagnet and the lower electromagnet are in differential control to form a pair to form an electromagnetic actuator, the plurality of electromagnetic actuators work cooperatively to suspend and support the supporting frame by means of electromagnetic force, axial displacement of the supporting frame is collected by a displacement sensor and is compared with a reference position to obtain deviation, the deviation is input to a high static low controller, the high static low controller outputs control voltage to a power amplifier, and control current of each electromagnet is formed to control the size of each electromagnetic attraction.
As shown in fig. 4, the high-static-low controller includes two links, a differential link and a gain link, which are respectively used to adjust the stiffness and damping characteristics of the dynamic system. The gain element comprises: substituting the deviation value into a gain link function expression fp(e) And calculating to obtain the control quantity of a gain link for adjusting the rigidity of the dynamic supporting system, wherein the differential link comprises the following steps: the deviation value is compared and multiplied by k corresponding to the differential parameter groupd1、kd2Differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system;
as shown in fig. 5, the high-static-low controller includes two links, a differential link and a gain link, which are respectively used to adjust the stiffness and damping characteristics of the dynamic system. The gain element comprises: substituting the deviation value into a gain link function expression fp(e) And calculating to obtain the control quantity of a gain link for adjusting the rigidity of the dynamic supporting system, wherein the differential link comprises the following steps: multiplying the deviation value by a differential link function expression fd(e) And then differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system.
Wherein k isaIs the power amplifier gain, ksIs the sensor gain, s is the Laplace operator, L is the external disturbance, kx、kIForce-displacement coefficient and force-current coefficient, m, respectivelyeThe mass of a load to be borne by a single electromagnetic actuator, Fe is electromagnetic force, x is the displacement of an object relative to an equilibrium position, Ref is a reference position, e is deviation, and e is Ref-x.
Before the high static low controller is used, the high static low control algorithm shown in fig. 4 or 5 is programmed into the controller, so that the whole closed-loop control system has the force-displacement nonlinear dynamic characteristic curve shown in fig. 6. Namely, it is
When the vibration occurs in the foundation or the supporting object, the amplitude of the reciprocating motion is generally smaller, the rigidity in the area near the equilibrium position of the vibration isolation system with high static and low dynamic characteristics is also smaller, and the vibration isolation principle shows that when the frequency of the vibration exciting force is higher than the natural frequency of the supporting system
In times, the system vibration can be effectively isolated, so that the lower the system natural frequency is under the condition of ensuring the bearing capacity, the better the system natural frequency is, and the expression of the support system natural frequency is as follows:
where k is the system stiffness, meFor the load mass required to be borne by a single electromagnetic actuator, the smaller the system rigidity is, the smaller the natural frequency of the supporting system is, and therefore, the low dynamic rigidity of the high static low dynamic system can play a role in effectively isolating vibration.
When impact acts on a foundation or a supporting object, the motion amplitude of the supporting object is generally larger, the supporting force increases/decreases along with the increase/decrease of the displacement and nonlinear rapid increase/decrease outside the vibration isolation system area with high static and low dynamic characteristics, the high static bearing force can effectively inhibit the displacement of the supporting object, on one hand, the vibration isolation system can effectively isolate vibration without losing the bearing force, and on the other hand, the influence of the impact load on the supporting object is reduced.
The active controllability of the electromagnetic actuator is utilized, and the nonlinear dynamic characteristics of high static and low dynamic of the electromagnetic actuator, namely high static bearing capacity and low dynamic stiffness, are realized by using a control algorithm. In operation, the vibration isolator (including the electromagnetic actuator and the support) in the system is placed between the supporting object and the foundation, and when the foundation or the supporting object vibrates, the low dynamic stiffness can play a role in effectively isolating the vibration. When impact acts on a foundation or a supporting object, the nonlinear rapid increase of the supporting force along with the increase of the relative displacement can effectively inhibit the displacement. The nonlinear vibration isolator not only can guarantee excellent vibration isolation and impact resistance while considering bearing capacity, but also can freely design and change a nonlinear dynamics characteristic curve of the vibration isolator according to actual structural parameters through the active control algorithm, is applied to different machines and working conditions, and can effectively reduce the influence of vibration and impact on a system.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is intended to include such modifications and variations.
Claims (7)
1. A nonlinear vibration isolation and shock resistance control system, comprising: a vibration isolation system, the vibration isolation system comprising: the electromagnetic actuator consists of an upper electromagnet and a lower electromagnet which are controlled in a differential mode, a displacement sensor is arranged in the middle of each electromagnet, the displacement sensors are connected with the signal conditioning circuit, and the power amplifier is connected with a coil of each electromagnet; the control system further comprises:
the first design module is used for designing a force-displacement nonlinear dynamic characteristic curve with high static and low dynamic characteristics according to different vibration and impact load working conditions, determining the size of a first displacement range and the segmentation number j of differential links, and determining the segmentation parameter set lambdaηWherein η ═ 1, 2.. j-1;
the second design module is used for obtaining the load bearing quality required by a single electromagnetic actuator according to the number of the electromagnetic actuators and the sum of the support frame and the load quality;
a first setting module for setting a gain link function expression f in a high static low control algorithm according to the coefficient in the force-displacement nonlinear dynamics characteristic curvep(e)；
A second setting module, configured to set a differential parameter set k in a differential link in the high static-low control algorithm according to a damping ratio requirement of an engineering applicationdηOr setting a differential link function expression f in the high static low control algorithmd(e) Wherein η ═ 1, 2.. j;
the writing module is used for programming and writing the set high static and low control algorithm into a controller of the vibration isolation system to form a high static and low controller;
the electromagnetic actuator is used for carrying out suspension support on the supporting frame through electromagnetic force generated by the cooperative work;
the displacement sensor is used for acquiring an axial displacement signal of the supporting frame and inputting the axial displacement signal into the signal conditioning circuit;
the signal conditioning circuit is used for converting the axial displacement signal from an analog quantity to a digital quantity and inputting the digital quantity to the high-static-low controller;
the high static low controller is used for comparing the received axial displacement with a reference position to obtain a deviation value, and the gain link function expression f is usedp(e) And the differential parameter group kdηOr with said differential link function expression fd(e) Calculating and generating a corresponding control signal, and inputting the control signal into the power amplifier;
the power amplifier generates control current according to the control signal, controls the attractive force of the electromagnetic actuator on the supporting frame, and adjusts the axial displacement of the supporting frame;
the force-displacement nonlinear dynamics characteristic curve is a curve expressed by a cubic function of the following formula,
y＝Ax3+Bx2+Cx+D
a, B, C, D is a coefficient of a cubic function determined from the curve, the cubic function satisfying: 3. Ax2+2·Bx+C≥0；
The high static low control algorithm comprises:
and a gain link:
substituting the deviation value into the gain link function expression fp(e) Calculating gain link control quantity to adjust the rigidity of the dynamic support system;
and (3) differentiation:
comparing the deviation value multiplied by the set of differential parameters kdηInner corresponding kd1、kd2、kd3…kdjThen, differentiation is carried out to obtain the control quantity of a differential link for adjustingDamping characteristics of the nodal dynamic bearing system; or
Multiplying the deviation value by the differential link function expression fd(e) Then, differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system;
taking the sum of the gain link control quantity and the differential link control quantity as the total high-static low controller output quantity;
the gain link function expression fp(e) Comprises the following steps:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kxIs the force-displacement coefficient, kIForce-current coefficient, e deviation value, A, B, C constant;
different deviation values and differential parameter groups k in the differential linkdηThe corresponding relation is as follows:
wherein λ isjFor the set of segmentation parameters, λ is satisfied1≤λ2≤λ3≤λ4≤...λj-1The number of segments j is more than or equal to 2 and the parameter set kdηThe setting of (1) satisfies:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kIIs the force-current coefficient, meThe mass of the load required for a single electromagnetic actuator, kpThe rigidity coefficient is related to the deviation value as follows:
wherein k issIs the displacement sensor gain, e is the offset value, A, B, C is a constant;
the differential element function expression fd(e) Comprises the following steps:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kIIs the force-current coefficient, meThe load mass required to be borne by a single electromagnetic actuator is provided, gamma is a damping ratio, and the range of gamma is more than 0 and less than 1.
2. The nonlinear vibration isolation and shock resistance control system of claim 1, wherein the first design module is further configured to: estimating the range of vibration response and impact response of the supported object;
the force-displacement nonlinear dynamics characteristic curve satisfies the following conditions: the estimated system stiffness in the region of the vibrational response near the equilibrium position is within a first range of displacement within a first range of stiffness; the system stiffness outside the region near the equilibrium position of the estimated impulse response is within a second range of displacement within a second range of stiffness; the system stiffness is the curvature of the force-displacement nonlinear dynamical characteristic curve;
the whole closed-loop control system has the force-displacement nonlinear dynamic characteristics of high static and low dynamic characteristics,
when a foundation or a supporting object is subjected to vibration load, the corresponding displacement of the foundation or the supporting object is within the first displacement range of the force-displacement nonlinear dynamic characteristic curve, the system stiffness of the vibration isolation system in the area near the equilibrium position is within a first stiffness range, according to the vibration isolation principle, the smaller the system stiffness is, the smaller the natural frequency of the vibration isolation system is, and according to the classical vibration theory, the wider the vibration isolation frequency band is, the better the vibration isolation effect is;
when impact acts on a foundation or a supporting object, the corresponding displacement of the impact is within the second displacement range of the force-displacement nonlinear dynamic characteristic curve, and the supporting force of the vibration isolation system within the second displacement range is increased/decreased in a nonlinear rapid mode along with the increase/decrease of the displacement.
3. The system of claim 2, wherein the single electromagnetic actuator is required to carry a load mass meThe following relationship is satisfied:
wherein m is the sum of the support frame and the load mass, and n is the number of the electromagnetic actuators.
4. The nonlinear vibration isolation and shock resistance control system of any one of claims 1-3, wherein the signal conditioning circuit comprises: the device comprises an AD conversion module and an AD sampling module, wherein the AD conversion module is used for converting the axial displacement signal from analog quantity to digital quantity, and the AD sampling module is used for setting sampling frequency and obtaining a final sampling signal from the axial displacement signal of the digital quantity;
the displacement sensor is as follows: the displacement sensor is an inductive sensor, the upper probe and the lower probe are controlled to collect through differential motion, and when the displacement sensor is an eddy current sensor, the upper probe and the lower probe are controlled to collect through one probe.
5. A nonlinear vibration isolation and shock resistance control method is applied to a vibration isolation system, and the vibration isolation system comprises: the electromagnetic actuator consists of an upper electromagnet and a lower electromagnet which are controlled in a differential mode, a displacement sensor is arranged in the middle of each electromagnet, the displacement sensors are connected with the signal conditioning circuit, and the power amplifier is connected with a coil of each electromagnet; the electromagnetic actuator is used for carrying out suspension support on the supporting frame through electromagnetic force generated by the cooperative work;
the control method comprises the following steps:
s1, designing a force-displacement nonlinear dynamic characteristic curve with high static and low dynamic characteristics according to different vibration and impact load working conditions, determining the size of a first displacement range and the number j of segments of a differential link, and determining the group lambda of segment parametersηWherein η ═ 1, 2.. j-1;
s2, obtaining the load mass required to be borne by a single electromagnetic actuator according to the number of the electromagnetic actuators and the sum of the support frame and the load mass;
s3, setting a gain link function expression f in a high static low control algorithm according to the coefficient in the force-displacement nonlinear dynamic characteristic curvep(e)；
S4, setting a differential parameter group k in a differential link in the high static low control algorithm according to the damping ratio requirement of engineering applicationdηOr setting a differential link function expression f in the high static low control algorithmd(e) Wherein η ═ 1, 2.. j;
s5, programming and writing the set high static and low control algorithm into a controller of the vibration isolation system to form a high static and low controller;
s6, the displacement sensor collects an axial displacement signal of the supporting frame and inputs the axial displacement signal into the signal conditioning circuit;
s7, converting the axial displacement signal from an analog quantity to a digital quantity by the signal conditioning circuit and inputting the digital quantity to the high static low controller;
s8, the high static low controller compares the received axial displacement with a reference position to obtain a deviation value, and the gain link function expression f is usedp(e) And the differential parameter group kdηOr with said differential link function expression fd(e) Calculate and generate correspondingA control signal, and inputting the control signal into the power amplifier;
s9, the power amplifier generates a control current according to the control signal and controls the attractive force of the electromagnetic actuator on the supporting frame;
the force-displacement nonlinear dynamics characteristic curve is a curve expressed by a cubic function of the following formula,
y＝Ax3+Bx2+Cx+D
a, B, C, D is a coefficient of a cubic function determined from the curve, the cubic function satisfying: 3. Ax2+2·Bx+C≥0；
The high static low control algorithm comprises:
and a gain link:
substituting the deviation value into the gain link function expression fp(e) Calculating gain link control quantity to adjust the rigidity of the dynamic support system;
and (3) differentiation:
comparing the deviation value multiplied by the set of differential parameters kdηInner corresponding kd1、kd2、kd3…kdjThen, differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system; or
Multiplying the deviation value by the differential link function expression fd(e) Then, differentiating to obtain a differential link control quantity for adjusting the damping characteristic of the dynamic support system;
taking the sum of the gain link control quantity and the differential link control quantity as the total high-static low controller output quantity;
the gain link function expression fp(e) Comprises the following steps:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kxIs the force-displacement coefficient, kIForce-current coefficient, e deviation value, A, B, C constant;
different deviation values and differential parameter groups k in the differential linkdηThe corresponding relation is as follows:
wherein λ isjFor the set of segmentation parameters, λ is satisfied1≤λ2≤λ3≤λ4≤...λj-1The number of segments j is more than or equal to 2 and the parameter set kdηThe setting of (1) satisfies:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kIIs the force-current coefficient, meThe mass of the load required for a single electromagnetic actuator, kpThe rigidity coefficient is related to the deviation value as follows:
wherein k issIs the displacement sensor gain, e is the offset value, A, B, C is a constant;
the differential element function expression fd(e) Comprises the following steps:
wherein k isaIs the power amplifier gain, ksIs the displacement sensor gain, kIIs the force-current coefficient, meThe load mass required to be borne by a single electromagnetic actuator is provided, gamma is a damping ratio, and the range of gamma is more than 0 and less than 1.
6. The method for controlling nonlinear vibration isolation and shock resistance according to claim 5, wherein the step S1 further comprises: estimating the range of vibration response and impact response of the supported object;
the force-displacement nonlinear dynamics characteristic curve satisfies the following conditions: the estimated system stiffness in the region of the vibrational response near the equilibrium position is within a first range of displacement within a first range of stiffness; the system stiffness outside the region near the equilibrium position of the estimated impulse response is within a second range of displacement within a second range of stiffness; the system stiffness is the curvature of the force-displacement nonlinear dynamical characteristic curve;
the whole closed-loop control system has the force-displacement nonlinear dynamic characteristics of high static and low dynamic characteristics,
when a foundation or a supporting object is subjected to vibration load, the corresponding displacement of the foundation or the supporting object is within the first displacement range of the force-displacement nonlinear dynamic characteristic curve, the system stiffness of the vibration isolation system in the area near the equilibrium position is within a first stiffness range, according to the vibration isolation principle, the smaller the system stiffness is, the smaller the natural frequency of the vibration isolation system is, and according to the classical vibration theory, the wider the vibration isolation frequency band is, the better the vibration isolation effect is;
when impact acts on a foundation or a supporting object, the corresponding displacement of the impact is within the second displacement range of the force-displacement nonlinear dynamic characteristic curve, and the supporting force of the vibration isolation system within the second displacement range is increased/decreased in a nonlinear rapid mode along with the increase/decrease of the displacement.
7. The method of claim 6, wherein the vibration isolation and impact resistance control is performed by a vibration isolation and impact resistance control device,
mass m of load to be borne by a single electromagnetic actuatoreThe following relationship is satisfied:
wherein m is the sum of the support frame and the load mass, and n is the number of the electromagnetic actuators.
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